<h2>题目编号 : 174</h2>
<div style="color:#666;font-size:80%;">22 December 2007</div><br />
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<p>We shall define a square lamina to be a square outline with a square &quot;hole&quot; so that the shape possesses vertical and horizontal symmetry.</p>
<p>Given eight tiles it is possible to form a lamina in only one way: 3x3 square with a 1x1 hole in the middle. However, using thirty-two tiles it is possible to form two distinct laminae.</p>
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<img src="project/images/p_173_square_laminas.gif" alt="" />
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<p>If <var>t</var> represents the number of tiles used, we shall say that <var>t</var> = 8 is type L(1) and <var>t</var> = 32 is type L(2).</p>
<p>Let N(<var>n</var>) be the number of <var>t</var> <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> 1000000 such that <var>t</var> is type L(<var>n</var>); for example, N(15) = 832.</p>
<p>What is <img src='images/symbol_sum.gif' width='11' height='14' alt='&sum;' border='0' style='vertical-align:middle;' /> N(<var>n</var>) for 1 <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> <var>n</var> <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> 10?</p>
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